Challenging question for you guys... Determine all pairs (n; p) of positive integers such that
p is a prime,n not exceeded 2p, and(p - 1)^n + 1 is divisible by n^(p-1).

Question

Challenging question for you guys... Determine all pairs (n; p) of positive integers such that
p is a prime,n not exceeded 2p, and(p - 1)^n  + 1 is divisible by n^(p-1).

anonymous · Answer

what is ¡

anonymous · Answer

dont think that came out properly...

anonymous · Answer

ok i tis meant to be (p-1) ^(n+1) and is divisible by n^(p-1)

anonymous · Answer

there i edited it... btw it is extremely challenging...

anonymous · Answer

looks like...:)

anonymous · Answer

Well, there can't be many....

anonymous · Answer

OK, now I found a similar question with (p-1)^n +1   ie not (p-1)^(n+1)

anonymous · Answer

from a test

anonymous · Answer

could u plz check the question again i think its (p-1)^n +1 not  (p - 1)^(n + 1)

anonymous · Answer

sorry my bad @mukushla

anonymous · Answer

its IMO 1999 problem 4 and solutions are
(2,2),(3,3),(1,q)  q:any prime number

anonymous · Answer

You can get 1,p and 2,2 by inspection the trickier part is to show the last one and as being the only other

anonymous · Answer

http://www.cs.cornell.edu/~asdas/imo/imo/isoln/isoln994.html